Three-Dimensional Relativistic MHD Simulations of the Kelvin-Helmholtz Instability: Magnetic Field Amplification by a Turbulent Dynamo

TL;DR

This paper uses 3D relativistic MHD simulations to show how turbulent dynamos triggered by Kelvin-Helmholtz instabilities can significantly amplify magnetic fields in relativistic outflows like GRBs and AGN.

Contribution

It demonstrates the magnetic field amplification mechanism via turbulent dynamo in relativistic shear flows, with implications for astrophysical jet phenomena.

Findings

Magnetic energy amplifies rapidly due to turbulence and saturates at a significant level.

The electromagnetic energy fraction reaches about 5 x 10^{-3} in simulated conditions.

The electromagnetic energy spectrum is flat, with most energy at small scales.

Abstract

Magnetic field strengths inferred for relativistic outflows including gamma-ray bursts (GRB) and active galactic nuclei (AGN) are larger than naively expected by orders of magnitude. We present three-dimensional relativistic magnetohydrodynamics (MHD) simulations demonstrating amplification and saturation of magnetic field by a macroscopic turbulent dynamo triggered by the Kelvin-Helmholtz shear instability. We find rapid growth of electromagnetic energy due to the stretching and folding of field lines in the turbulent velocity field resulting from non-linear development of the instability. Using conditions relevant for GRB internal shocks and late phases of GRB afterglow, we obtain amplification of the electromagnetic energy fraction to $\epsilon_B \sim 5 \times 10^{-3}$. This value decays slowly after the shear is dissipated and appears to be largely independent of the initial field strength. The conditions required for operation of the dynamo are the presence of velocity shear and some seed magnetization both of which are expected to be commonplace. We also find that the turbulent kinetic energy spectrum for the case studied obeys Kolmogorov's 5/3 law and that the electromagnetic energy spectrum is essentially flat with the bulk of the electromagnetic energy at small scales.